There are three main formats, GIF JPG and PNG. Each has a varity of properties and care must be taken when choosing which format to use.
GIF (compuserve Graphic Interchange Format)
Great for animated images, reducing the number of colors used reduces the file size, so a black and white diagram can be saved as a two color image. GIF can be saved as dithered, where it atempts to smooth the graphic and it can be saved as interlaced or not. This has just to do with the way the image will load in a browser. If non interlaced it displays the picture as it is loading from top to bottom. If interlaced then it will build the picture from horizontal bands.
JPG
Great for photos or gradient graphics. Has a varible compression ratio algorithm that allows you to adjust the degree of applied compression. Experiment to get the best result. Keep an original copy of your graphic in a non lossy format eg PNG or BMP because a picture saved as JPG will lose detail.
PNG (portable Network Graphics)
Is the newest format. It will compress the graphic to a degree but will not degredate the image quality from the original. It is also big on transparancy.